Solve -2x/x-y/frac{y{x^2}}

$$\frac{ \frac{ -2x }{ x-y } }{ \frac{ y }{ { x }^{ 2 } } }$$

Evaluate

$$-\frac{2x^{3}}{y\left(x-y\right)}$$

Short Solution Steps

Divide \frac{-2x}{x-y} by \frac{y}{x^{2}} by multiplying \frac{-2x}{x-y} by the reciprocal of \frac{y}{x^{2}}.

$$\frac{-2xx^{2}}{\left(x-y\right)y}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-2x^{3}}{\left(x-y\right)y}$$

Use the distributive property to multiply x-y by y.

$$\frac{-2x^{3}}{xy-y^{2}}$$

Differentiate w.r.t. x

$$\frac{2\times \left(\frac{x}{x-y}\right)^{2}\left(3y-2x\right)}{y}$$